Difference between revisions of "Derivative"
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| − | Let $ | + | Let $D$ be a subset of [[complex number|complex numbers]], $z_0 \in D$, and let $f \colon D \rightarrow \mathbb{C}$ be a [[function]]. We say that $f$ is (complex-) differentiable at $z_0$ if the [[limit]] |
| − | $$f'( | + | $$f'(z_0)=\displaystyle\lim_{h \rightarrow 0} \dfrac{f(z_0+h)-f(z_0)}{h}$$ |
exists. | exists. | ||
=Properties= | =Properties= | ||
| − | + | [[Derivative is a linear operator]]<br /> | |
| − | + | [[Relationship between q-derivative and derivative]] | |
Latest revision as of 05:10, 26 November 2016
Let $D$ be a subset of complex numbers, $z_0 \in D$, and let $f \colon D \rightarrow \mathbb{C}$ be a function. We say that $f$ is (complex-) differentiable at $z_0$ if the limit $$f'(z_0)=\displaystyle\lim_{h \rightarrow 0} \dfrac{f(z_0+h)-f(z_0)}{h}$$ exists.
Properties
Derivative is a linear operator
Relationship between q-derivative and derivative
